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There are several evidences of the hadronic total cross section σtot to be proportional to B log2s consistent with the Froissart unitarity bound. The COMPETE collaboration has further assumed σtot ≃ B log2(s/s0) + Z to extend its universal rise with the common value of B for all hadronic scatterings to reduce the number of adjustable parameters. The coefficient B is suggested to be universal in the arguments of color glass condensate (CGC) of QCD. There has been, however, no rigorous proof yet based only on QCD. We attempt to investigate the values of B for πxxxp, Kxxxp and p¯p, pp scatterings respectively through the search for the simultaneous best fit to the experimental σtot and ρ ratios at high energies. The σtot at the resonance and intermediate energy regions has also been exploited as a duality constraint based on the special form of finite-energy sum rule (FESR). We estimate the values of B individually for πxxxp, Kxxxp and p¯p, pp scatterings without using the universality hypothesis. It turs out that the values of B are mutually consistent within one standard deviation, and the universal rise of hadronic total cross sections is strongly suggested. It has to be stressed that we cannot obtain such a definite conclusion without the duality constraint.

Test of Universal Rise of Hadronic Total Cross Sections Based on πp, Kp, \-pp and pp Scatterings